Minimizing leakage around the tips of compressor and/or turbine blades in gas turbine engines or other turbomachines improves efficiency. In most prior active tip clearance control proposals, a shroud or surface thereof is moved toward and away from blade tips during engine operation to maintain predetermined tip clearance. For example, many prior proposals include a thermally responsive shroud around blade tips which shroud expands and contracts in accordance with selective exposure to hot gas behind the shroud. In another proposal, the inside diameter of a segmented shroud is controlled by balancing high pressure air in a chamber behind the shroud against normal gas pressure on the opposite side of the shroud in a gas flow path of the turbomachine. In still other proposals, mechanical linkages and eccentrics bodily shift annular shrouds longitudinally toward and away from the blade tips. And in yet another proposal, a shroud wall of a radial flow compressor is connected to a static support through a flexible diaphragm which distorts under thermal and pressure loading to effect movement of the shroud wall. A gas turbine engine or turbomachine according to this invention includes novel, active tip clearance control apparatus.